Flexible redundant array of independent disks (raid) computation device

ABSTRACT

A method for calculating a plurality (M) of redundancy blocks for multiple (N) data blocks of a plurality (D) of words each, the method comprises: receiving the number (M) of redundancy blocks by a calculator that comprises multiple (R) calculation units; configuring the calculator according to M and R; concurrently calculating, if M equals R, by the multiple (R) calculation units of the calculator, R sets of parity vectors, each set includes a plurality (D) of parity vectors; and calculating the plurality (M) of the redundancy blocks based on the R sets of parity vectors.

FIELD OF THE INVENTION

The invention relates to calculation of redundancy blocks for datablocks.

BACKGROUND OF THE INVENTION

The amount of data stored in today's data-centers is rapidly growing,while reliability is becoming more important than ever before.

As a result, storage density is also growing, while disk failure rate isnot improving.

This poses major scalability challenges on redundant array ofindependent disks (RAID) redundancy scheme, due to the increased numberof disks, and increased chance for double and triple faults during longdisk rebuild times.

RAID 5 calculates a single parity block for multiple data blocks.

The parity block is calculated as the XOR of all data blocks. RAID 5provides an ability to recover from a single disk failure. Thereconstruction of a failed disk requires reading all other disks. Thereis a relatively high risk for a second disk failure during thereconstruction of the failed disk.

RAID 6 calculates a pair of parity blocks for multiple data blocks.Parity blocks are calculated as XOR and Galois field (GF) multiplicationof all data blocks.

RAID 6 provides the ability to recover from up to 2 disk failures. Thereconstruction failed disks requires reading all other disks. It wasbelieved to have relatively low risk for a third disk to fail during thereconstruction of two failed disks.

Current solutions for data protection were tailored to a specific RAIDlevel (RDID 5, RAID 6 . . . ).

There is a growing need to provide efficient systems and methods forcalculating redundancy in a flexible manner.

SUMMARY OF THE INVENTION

According to various embodiments of the invention there are providedmethods and devices.

According to various embodiments of the invention there may be provideda method for calculating a plurality (M) of redundancy blocks formultiple (N) data blocks of a plurality (D) of words each, the methodmay include receiving the number (M) of redundancy blocks by acalculator that may include multiple (R) calculation units; configuringthe calculator according to M and R; concurrently calculating, if Mequals R, by the multiple (R) calculation units of the calculator, Rsets of parity vectors, each set includes a plurality (D) of parityvectors; and calculating the plurality (M) of the redundancy blocksbased on the R sets of parity vectors.

The method may include concurrently calculating, if M is smaller than R,by a subset of M calculation units of the calculator, M sets of parityvectors, each set includes a plurality (D) of parity vectors; andcalculating the plurality (M) of the redundancy blocks based on the Msets of parity vectors.

The method may include calculating, if M equals one, by a singlecalculation unit of the calculator, a single set of parity vectors thatincludes a plurality (D) of parity vectors; and calculating a redundancyblock based on the set of parity vectors.

If M exceeds R and M modulo R equals a difference X, then the method mayinclude selecting a certain set of R rows of a Vandermonde matrix;concurrently calculating by the multiple (R) calculation units of thecalculator, R sets of parity vectors, each set includes a plurality (D)of parity vectors; wherein the calculating may include processing thecertain set of R rows of the Vandermonde matrix.

If there are more than R rows of the Vandermonde matrix that were notprocessed then the method may include selecting a new certain set of Rrows of the Vandermonde matrix and concurrently calculating by themultiple (R) calculation units of the calculator, new R sets of parityvectors; wherein the calculating may include processing the new certainset of R rows of the Vandermonde matrix.

If there are X rows of the Vandermonde matrix that were not processedthen the method may include selecting a further certain set of X rows ofthe Vandermonde matrix and concurrently calculating by X calculationunits of the calculator, further X sets of parity vectors; wherein thecalculating may include processing the further certain set of R rows ofthe Vandermonde matrix; and calculating M redundancy blocks based on allsets of the parity vectors.

Different calculation units may calculate different sets of parityvectors by multiplying different rows of a Vandermonde matrix byintermediate vectors driven from the multiple data blocks.

Different values of M may represent different redundant array ofindependent disks (RAID) levels.

The R may be not smaller than four.

If M exceeds R then the method may include calculating up to R parityblocks at a time until calculating the zeroeth till (M−1)'th parityblock.

The buffer has a buffer size, and wherein the configuring may includedetermining a size of the data block in response to a ratio between thebuffer size and a number of activated calculation units.

The method may include receiving multiple coefficients of theVandermonde matrix in descriptors of the data blocks.

The adding may be executed by exclusive OR (XOR) gates.

According to various embodiments of the invention there may be provideda system for calculating a plurality (M) of redundancy blocks formultiple (N) data blocks of a plurality (D) of words each, the systemmay include a memory unit that is arranged to receive the number (M) ofredundancy blocks; a calculator that may include multiple (R)calculation units; a controller that is arranged to configure thecalculator according to M and R; wherein the multiple (R) calculationunits may be arranged to concurrently calculate, if M equals R, R setsof parity vectors, each set includes a plurality (D) of parity vectors;and wherein the calculator is further arranged to calculate theplurality (M) of the redundancy blocks based on the R sets of parityvectors.

If M is smaller than R, then a subset of M calculation units of thecalculator may be arranged to calculate M sets of parity vectors, eachset includes a plurality (D) of parity vectors; and wherein thecalculator is further arranged to calculate the plurality (M) of theredundancy blocks based on the M sets of parity vectors.

If M equals one, then a single calculation unit of the calculator isarranged to calculate a single set of parity vectors that includes aplurality (D) of parity vectors;

and wherein the calculator is further arranged to calculate a redundancyblock based on the set of parity vectors.

If M exceeds R and M modulo R equals a difference X, then the controlleris arranged to select a certain set of R rows of a Vandermonde matrix;wherein the multiple (R) calculation units may be arranged toconcurrently calculate R sets of parity vectors, each set includes aplurality (D) of parity vectors; wherein the calculating may includeprocessing the certain set of R rows of the Vandermonde matrix.

If there are more than R rows of the Vandermonde matrix that were notprocessed then the controller is arranged to select a new certain set ofR rows of the Vandermonde matrix and wherein the multiple (R)calculation units may be arranged to concurrently calculate new R setsof parity vectors; wherein the calculating may include processing thenew certain set of R rows of the Vandermonde matrix.

If there are X rows of the Vandermonde matrix that were not processedthen the controller is arranged to select a further certain set of Xrows of the Vandermonde matrix and X calculation units may be arrangedto calculate further X sets of parity vectors; wherein the calculatingmay include processing the further certain set of R rows of theVandermonde matrix; and wherein the calculator is further arranged tocalculate M redundancy blocks based on all sets of the parity vectors.

Different calculation units may be arranged to calculate different setsof parity vectors by multiplying different rows of a Vandermonde matrixby intermediate vectors driven from the multiple data blocks.

Different values of M may represent different redundant array ofindependent disks (RAID) levels.

According to various embodiments of the invention there may be provideda method for reconstructing multiple (N) information blocks of aplurality (D) of words each, the method may include receiving a value ofN, by a calculator that may include multiple (R) calculation units;wherein the multiple information blocks are selected of a group of N+Minformation blocks, the group of (N+M) information blocks may include Ndata blocks and M parity blocks; configuring the calculator according toN and R; concurrently calculating, if N equals R, by the multiple (R)calculation units of the calculator, R sets of reconstructed datavectors, each set includes a plurality (D) of reconstructed datavectors; and generating N reconstructed data blocks based on the R setsof reconstructed data vectors.

The method may include concurrently calculating, if N is smaller than R,by a subset of N calculation units of the calculator, N sets ofreconstructed data vectors, each set includes a plurality (D) ofreconstructed data vectors; and calculating the multiple (N)reconstructed data blocks based on the N sets of reconstructed datavectors.

The method may include calculating, if N equals one, by a singlecalculation unit of the calculator, a single set of reconstructed datavectors that includes a plurality (D) of reconstructed data vectors; andcalculating a reconstructed data block based on the set of reconstructeddata vectors.

If N exceeds R and N modulo R equals a difference X, then the method mayinclude selecting a certain set of R rows of an inverted matrix; theinverted matrix is calculated by inverting a reduced matrix, the reducedmatrix is calculated by reducing M rows of an input matrix that mayinclude (N+M) rows, the input matrix may include a first group of N rowsand a second group of M rows, the first group of rows form a unitymatrix, the second group of rows form a Vandermonde matrix; concurrentlycalculating by the multiple (R) calculation units of the calculator, Rsets of reconstructed data vectors, each set includes a plurality (D) ofreconstructed data vectors; wherein the calculating may includeprocessing the certain set of R rows of the inverted matrix.

If there are more than R rows of the inverted matrix that were notprocessed then the method may include selecting a new certain set of Rrows of the Inverted matrix and concurrently calculating by the multiple(R) calculation units of the calculator, new R sets of reconstructeddata vectors; wherein the calculating may include processing the newcertain set of R rows of the Inverted matrix.

If there are X rows of the Inverted matrix that were not processed thenthe method may include selecting a further certain set of X rows of theInverted matrix and concurrently calculating by X calculation units ofthe calculator, further X sets of reconstructed data vectors; whereinthe calculating may include processing the further certain set of R rowsof the Inverted matrix; and calculating N redundancy blocks based on allsets of the reconstructed data vectors.

Different calculation units calculate different sets of reconstructeddata vectors by multiplying different rows of the inverted matrix byintermediate vectors driven from the multiple reconstructed data blocks.

R may not be smaller than four.

If N exceeds R then the method may include calculating up to Rreconstructed data blocks at a time until calculating the zeroeth till(N−1)'th reconstructed data block.

The buffer has a buffer size, and the configuring may includedetermining a size of the reconstructed data block in response to aratio between the buffer size and a number of activated calculationunits.

The method may include receiving multiple coefficients of the Invertedmatrix in descriptors of the information blocks.

The adding may be executed by exclusive OR (XOR) gates.

According to various embodiments of the invention there may be provideda system reconstructing multiple (N) information blocks of a plurality(D) of words each, the system may include a memory unit adapted toreceive a value of N; a calculator that may include multiple (R)calculation units; a controller that is arranged to configure thecalculator in response to R and N; wherein the multiple calculationunits may be arranged to concurrently calculate, if N equals R, by themultiple (R) calculation units of the calculator, R sets ofreconstructed data vectors, each set includes a plurality (D) ofreconstructed data vectors; and wherein the calculator is furtherarranged to generate N reconstructed data blocks based on the R sets ofreconstructed data vectors; wherein the multiple information blocks areselected of a group of (N+M) information blocks, the group of (N+M)information blocks may include N data blocks and M parity blocks.

If N is smaller than R, then a subset of N calculation units of thecalculator may be arranged to calculate N sets of reconstructed datavectors, each set includes a plurality (D) of reconstructed datavectors; and wherein the calculator is further arranged to calculate theplurality (N) of the reconstruction blocks based on the N sets ofreconstructed data vectors.

If N equals one, then a single calculation unit of the calculator isarranged to calculate a single set of reconstructed data vectors thatincludes a plurality (D) of reconstructed data vectors; and wherein thecalculator is further arranged to calculate a reconstruction block basedon the set of reconstructed data vectors.

If N exceeds R and N modulo R equals a difference X, then the controlleris arranged to select a certain set of R rows of an inverted matrix; theinverted matrix is calculated by inverting a reduced matrix, the reducedmatrix is calculated by reducing

M rows of an input matrix that may include (N+M) rows, the input matrixmay include a first group of N rows and a second group of M rows, thefirst group of rows form a unity matrix, the second group of rows form aVandermonde matrix; wherein the multiple (R) calculation units may bearranged to concurrently calculate R sets of reconstructed data vectors,each set includes a plurality (D) of reconstructed data vectors; whereinthe calculating may include processing the certain set of R rows of theInverted matrix.

If there are more than R rows of the Inverted matrix that were notprocessed then the controller is arranged to select a new certain set ofR rows of the inverted matrix and wherein the multiple (R) calculationunits may be arranged to concurrently calculate new R sets ofreconstructed data vectors; wherein the calculating may includeprocessing the new certain set of R rows of the inverted matrix.

If there are X rows of the inverted matrix that were not processed thenthe controller is arranged to select a further certain set of X rows ofthe inverted matrix and X calculation units may be arranged to calculatefurther X sets of reconstructed data vectors; wherein the calculatingmay include processing the further certain set of R rows of the invertedmatrix; and wherein the calculator is further arranged to calculate Nreconstruction blocks based on all sets of the reconstructed datavectors.

Different calculation units may be arranged to calculate different setsof reconstructed data vectors by multiplying different rows of theinverted matrix by intermediate vectors driven from the multiplereconstructed data blocks.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features, and advantages of the presentinvention will become more apparent from the following detaileddescription when taken in conjunction with the accompanying drawings. Inthe drawings, similar reference characters denote similar elementsthroughout the different views, in which:

FIG. 1 illustrates a method according to an embodiment of the invention;

FIG. 2 illustrates a system according to an embodiment of the invention;

FIG. 3 illustrates data structures according to an embodiment of theinvention;

FIG. 4 illustrates a method according to an embodiment of the invention;

FIG. 5 illustrates data structures according to an embodiment of theinvention;

FIG. 6 illustrates data structures according to an embodiment of theinvention; and

FIG. 7 illustrates data structures according to an embodiment of theinvention.

DETAILED DESCRIPTION OF THE DRAWINGS

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However, it will be understood by those skilled in the art that thepresent invention may be practiced without these specific details. Inother instances, well-known methods, procedures, and components have notbeen described in detail so as not to obscure the present invention.

The subject matter regarded as the invention is particularly pointed outand distinctly claimed in the concluding portion of the specification.The invention, however, both as to organization and method of operation,together with objects, features, and advantages thereof, may best beunderstood by reference to the following detailed description when readwith the accompanying drawings.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

Because the illustrated embodiments of the present invention may for themost part, be implemented using electronic components and circuits knownto those skilled in the art, details will not be explained in anygreater extent than that considered necessary as illustrated above, forthe understanding and appreciation of the underlying concepts of thepresent invention and in order not to obfuscate or distract from theteachings of the present invention.

Any reference in the specification to a method should be applied mutatismutandis to a system capable of executing the method and should beapplied mutatis mutandis to a non-transitory computer readable mediumthat stores instructions that once executed by a computer result in theexecution of the method.

Any reference in the specification to a system should be applied mutatismutandis to a method that may be executed by the system and should beapplied mutatis mutandis to a non-transitory computer readable mediumthat stores instructions that may be executed by the system.

Any reference in the specification to a non-transitory computer readablemedium should be applied mutatis mutandis to a system capable ofexecuting the instructions stored in the non-transitory computerreadable medium and should be applied mutatis mutandis to method thatmay be executed by a computer that reads the instructions stored in thenon-transitory computer readable medium.

According to an embodiment of the invention there is provide a flexiblesystem that can be easily adjusted for calculating a large range ofredundancy schemes, a large range of code rates (code rate reflects arelationship between data and parity of an encoded unit), for performingparity calculations with different valued coefficients, for calculatingRAID calculations of different levels. The system has a paritycalculator that has R calculation units that may operate in parallel andwhen a number (M) of parity blocks exceeds R the system can calculateall the required M parity blocks in multiple iterations. The system canoffload both encoding and decoding (reconstruction), can performcalculations with configurable Galois Field generator polynomial byusing configurable logarithmic and anti-logarithmic conversions.

Multiple (N) data blocks, each of d words can be received. Multiple (M)parity blocks can be calculated to these multiple data blocks. Thenumber (M) of parity blocks is programmed and the following systems andmethods are capable of calculating different numbers of parity blocks ina flexible manner.

The rows of table 1 illustrate an example of multiple (N) data blocksDB(0)−DB(N−1). Data block BD(0) includes words W(0,0)−W(0,D−1), the(N−1)'th data block DB(N−1) includes words W(N−1,0)−W(N−1,D−1). Ingeneral, assuming index n that ranges between 0 and (N−1) then the n'thdata block DB(n) includes words W(n,0)−W(n,D−1) data block DB(1).

TABLE 1 W(0,0) W(0,1) W(0,D-1) W(1,0) W(1,1) W(1,D-1) W(N-1,0) W(N-1,1)W(N-1,D-1)

D intermediate vectors are defined VI(0)−VI(D−1), each intermediatevector includes a column of table 1:

VI(0)=(W(0,0), W(1,0) . . . W(N−1,0)).

VI(1)=(W(0,1), W(1,1) . . . W(N−1,1)).

VI(D−1)=(W(0,D−1), W(1,D−1) . . . W(N−1,D−1)).

In general, d ranging between zero and D−1, the d'th vector shouldequal: VI(d)=(W(0,d), W(1,d) . . . W(N−1,d)).

FIG. 3 illustrates four data blocks 321-324, that form four intermediatevectors 331-334.

M parity blocks PB(0)−PB(M−1) are calculated. This includes calculatingD parity vectors PV(0)−PV(D−1) (of M elements each) and rearranging theelements of these parity vectors to provide the M parity blocks—eachparity block of D elements.

If the M parity blocks are arranged to form a parity block matrix andthe D parity vectors are arranged to form a parity vector matrix thanthe columns of the parity vector matrix equal the rows of the parityblock matrix.

Assuming index d that ranges between 0 and D−1, the d'th parity vectorPV(d) is calculated by multiplying a d'th by a Vandermonde matrix (VM).The VM matrix has M rows and N columns. It includes M*N coefficients, asillustrated by table 2:

TABLE 2 VM(0,0) = 1⁰ VM(0,1) = 2⁰ VM(0,N-1) = N⁰ VM(1,0) = 1¹ VM(1,1) =2¹ VM(1,N-1) = N¹ VM(M-1,0) = 1^(M-1) VM(M-1,1) = 2^(M-1) VM(M-1,N-1) =N^(M-1)

In general, the (m,n)'th element of VM is a coefficient that equalsn^((m−1))

Each parity vector is calculated by multiplying VM by a correspondingintermediate vector VI.

Therefore:

PV(0)=VM*VI(0)

PV(1)=VM*VI(1)

PV(D−1)=VM*VI(D−1)

In general PV(d)=VM*VI(d).

Each element of each parity vector is a sum of n products ofmultiplications of elements of a single row of the Vandermonde matrixand the corresponding intermediate vector. These n multiplications canbe executed in an iterative manner—during each iteration an intermediateresult is added to a product of an element of the intermediate vectorand a Vandermonde matrix coefficient.

Accordingly:

PV(0,0)=VM(0,0)*W(0,0)+VM(0,1)*W(1,0)+ . . . +VM(0,N−1)*W(N−1,0).

PV(1,0)=VM(1,0)*W(0,0)+VM(1,1)*W(1,0)+ . . . +VM(1,N−1)*W(N−1,1).

PV(M−1,0)=VM(M−1,0)*W(0,0)+VM(M−1,1)*W(1,0)+ . . .+VM(M−1,N−1)*W(N−1,0).

PV(0,1)=VM(0,0)*W(0,1)+VM(0,1)*W(1,1)+ . . . +VM(0,N−1)*W(N−1,1).

PV(1,1)=VM(1,0)*W(0,1)+VM(1,1)*W(1,1)+ . . . +VM(1,N−1)*W(N−1,1).

PV(M−1,1)=VM(M−1,0)*W(0,1)+VM(M−1,1)*W(1,1)+ . . .+VM(M−1,N−1)*W(N−1,1).

PV(0,D−1)=VM(0,0)*W(0,D−1)+VM(0,1)*W(1,D−1)+ . . .+VM(0,N−1)*W(N−1,D−1).

PV(1,D−1)=VM(1,0)*W(0,D−1)+VM(1,1)*W(1,D−1)+ . . .+VM(1,N−1)*W(N−1,D−1).

PV(M−1,D−1)=VM(M−1,0)*W(0, D−1)+VM(M−1,1)*W(1,D−1)+ . . .+VM(M-LN−1)*W(N−1,D−1).

In general, the m'th element of the d'th parity vector PV(m,d) equalsVM(m,0)*W(0,d)+VM(m,1)*W(1,d)+ . . . +VM(m,N−1)*W(N−1,d).

Each element of each parity vector can be calculated by executing Ncalculations of the following:

-   -   a. Multiplying, by the r'th computational unit, an m'th row of        the Vandermonde matrix by the r'th element of all of the        intermediate vectors—by the r'th data block.

b. Adding the product to a previously calculated (that last calculated)result (for example—VM(m,1)*PI(d,1)) to provide an intermediate result.

After N repetitions the intermediate result is actually the finalresult—the element of the parity vector.

TABLE 3 illustrates multiple calculations that should be made forcalculating the first element of each parity vector:

TABLE 3 VM(0,0)*W(0,0) = PI(0,0) PI(0,0) + VM(0,1)*W(1,0) = PI(1,0)PI(0,N-2) + VM(0,N-1)*W(N-1,0) = PI(N-1,0) VM(0,0)*W(0,1) = PI(0,1)PI(1,0) + VM(0,1)*W(1,1) = PI(1,1) PI(1,N-2) + VM(0,N-1)*W(N-1,1) =PI(0,1) VM(0,0)*W(0,D-1) = PI(0,D-1) PI(D-1,0) + VM(0,1)*W(1,D-1) =PI(1,D-1) PI(D-1,N-2) + VM(0,N-1)*W(N-1,D-1) = PI(0,D-1)

In order to calculate the entire parity vectors these should be Mcalculations—each time with a different row of VM. Each one of thecomputational units of the calculator is arranged to calculate oneparity vector.

According to an embodiment of the invention the calculation of theparity vectors is executed in parallel by R calculation units. Assuming,for example, that R=M then during each calculation iteration a word ofdifferent intermediate vectors (originating from the same data block)are multiplied by different coefficients, so that during each iterationthe calculations that form a row of TABLE 3 are calculated.

Assuming that R=D=4 and M=2 then:

${{Vi}(0)} = \begin{matrix}{W\left( {0,0} \right)} \\{W\left( {1,0} \right)} \\{W\left( {2,0} \right)} \\{W\left( {3,0} \right)}\end{matrix}$ ${{Vi}(1)} = \begin{matrix}{W\left( {0,1} \right)} \\{W\left( {1,1} \right)} \\{W\left( {2,1} \right)} \\{W\left( {3,1} \right)}\end{matrix}$ ${{Vi}(2)} = \begin{matrix}{W\left( {0,2} \right)} \\{W\left( {1,2} \right)} \\{W\left( {2,2} \right)} \\{W\left( {3,2} \right)}\end{matrix}$ ${{Vi}(3)} = \begin{matrix}{W\left( {0,3} \right)} \\{W\left( {1,3} \right)} \\{W\left( {2,3} \right)} \\{W\left( {3,3} \right)}\end{matrix}$ ${VM} = {\begin{matrix}{{VM}\left( {0,0} \right)} & {{VM}\left( {0,1} \right)} & {{VM}\left( {0,2} \right)} & {{VM}\left( {0,3} \right)} \\{{VM}\left( {1,0} \right)} & {{VM}\left( {1,1} \right)} & {{VM}\left( {1,2} \right)} & {{VM}\left( {1,3} \right)}\end{matrix} = \begin{matrix}1 & 1 & 1 & 1 \\1 & 2 & 3 & 4\end{matrix}}$

The following take place:

-   -   a. A first calculation unit will calculate a first parity        vector. During four iterations it performs the following:        -   i. Multiply the first element (1) of the first row of            VM (1111) by the first element of each one of            VI(0)−VI(3)—which is actually the first data block—W(0,0),            W(0,1), W(0,2) and W(0,3) to provide first products            PD(0,0)−PD(0,3) which are also referred to as first            intermediate results PI(0,0)−PI(0,3) which are stored in a            first half of a buffer.        -   ii. Multiply the second element (1) of the first row of            VM (1111) by the second element of each one of            VI(0)−VI(3)—which is actually the second data block—W(1,0),            W(1,1), W(1,2) and W(1,3) to provide second products            PD(1,0)−PD(1,3), and add the first intermediate results            PI(0,0)−PI(0,3) to the second products PD(1,0)−PD(1,3) to            provide second intermediate results PI(1,0)−PI(1,3) which            are stored in a first half of the buffer.        -   iii. Multiply the third element (1) of the first row of            VM (1111) by the third element of each one of            VI(0)−VI(3)—which is actually the third data block—W(2,0),            W(2,1), W(2,2) and W(2,3) to provide third products            PD(2,0)−PD(2,3), and add the second intermediate results            PI(1,0)−PI(1,3) to the third products PD(2,0)−PD(2,3) to            provide third intermediate results PI(2,0)−PI(2,3) which are            stored in a first half of the buffer.        -   iv. Multiply the fourth element (1) of the first row of            VM (1111) by the fourth element of each one of            VI(0)−VI(3)—which is actually the fourth data block—W(3,0),            W(3,1), W(3,2) and W(3,3) to provide fourth products            PD(3,0)−PD(3,3), and add the third intermediate results            PI(2,0)−PI(2,3) to the fourth products PD(3,0)−PD(3,3) to            provide fourth intermediate results PI(3,0)−PI(3,3) which            are stored in a first half of the buffer and form the first            party vector.    -   b. A second calculation unit will calculate a second parity        vector. During four iterations it performs the following:        -   i. Multiply the first element (1) of the second row of            VM (1234) by the first element of each one of            VI(0)−VI(3)—which is actually the first data block—W(0,0),            W(0,1), W(0,2) and W(0,3) to provide first products            PD′(0,0)−PD′(0,3) which are also referred to as first            intermediate results PI′(0,0)−PI′(0,3) which are stored in a            second half of the buffer.        -   ii. Multiply the second element (2) of the second row of            VM (1234) by the second element of each one of            VI(0)−VI(3)−which is actually the second data block—W(1,0),            W(1,1), W(1,2) and W(1,3) to provide second products            PD′(1,0)−PD′(1,3), and add the first intermediate results            PI′(0,0)−PI′(0,3) to the second products PD′(1,0)−PD′(1,3)            to provide second intermediate results PI′(1,0)−PI′(1,3)            which are stored in a second half of the buffer.        -   iii. Multiply the third element (3) of the second row of            VM (1234) by the third element of each one of            VI(0)−VI(3)—which is actually the third data block—W(2,0),            W(2,1), W(2,2) and W(2,3) to provide third products            PD′(2,0)−PD′(2,3), and add the second intermediate results            PI′(1,0)−PI′(1,3) to the third products PD′(2,0)−PD′(2,3) to            provide third intermediate results PI′(2,0)−PI′(2,3) which            are stored in a second half of the buffer.        -   iv. Multiply the fourth element (4) of the second row of            VM (1234) by the fourth element of each one of            VI(0)−VI(3)—which is actually the fourth data block—W(3,0),            W(3,1), W(3,2) and W(3,3) to provide fourth products            PD′(3,0)−PD′(3,3), and add the third intermediate results            PI′ (2,0)−PI′(2,3) to the fourth products PD′(3,0)−PD′(3,3)            to provide fourth intermediate results PI′(3,0)−PI′(3,3)            which are stored in a second half of the buffer.            PI′(3,0)−PI′(3,3) form a second parity vector.    -   c. A first and second parity blocks will be driven from the        first and second parity vectors.

FIG. 3 illustrates a two-row and a four column Vandermonde matrix 310that includes row 311 and 312. FIG. 3 illustrates a calculation of fourproducts obtained by calculating VM(0,0) (denoted VM00) by the firstelement of each intermediate vector (W00, W01, W02 and W03) during afirst iteration and a calculation of four products by calculatingVM(0,1) (denoted VM01) by the second element of each intermediate vector(W10, W11, W12 and W13) during a second iteration.

FIG. 3 also shows two parity vectors 341-342, each of four elementsPV00-PV03 and PV10-PV13 respectively that are converted to four parityblocks 351-354 each of two elements each: (PV00, PV10), (PV01, PV11),(PV02, PV12) and (PV03, PV13).

FIG. 1 illustrates a method 100 according to an embodiment of theinvention.

Method 100 starts by stage 110 of receiving M and N and calculating orreceiving D. The maximum size of D is limited by a ratio between theavailable space of a buffer by M.

Stage 110 is followed by stage 120 of receiving N data blocks by acalculator that comprises multiple (R) calculation units, each datablock is D word long. Stage 120 may also include receiving VandermondeMatrix coefficients. The Vandermonde Matrix coefficients can be providedwithin descriptors of the data blocks or otherwise provided to thecalculation unit.

Stage 120 may be followed by stage 130 of converting the N data blocksto D intermediate vectors, wherein the d'th intermediate vector (index dranges between zero and D−1) includes the d'th words of each data block.

Stage 130 may be followed by stage 140 of configuring the calculatoraccording to M and R.

If R>M then a sub-set of M calculation units will be utilized.

If R=M all R calculation units will be utilized. If R<M then thefollowing stages will be executed in multiple iterations , each timeutilizing up to R calculation units for multiplying up to R rows of aVandermonde matrix by intermediate vectors. If, for example M=7 and R=4then during a first iteration four calculation units can be used tomultiply four rows of the 7×N Vandermonde matrix by intermediate vectorsand during another iteration three calculation units will be sued tomultiply the three remaining rows of the Vandermonde matrix byintermediate vectors.

Thus, stage 140 may include stage 142 of checking if M exceeds R.

If M does not exceed R then jumping to stage 150 of concurrentlycalculating, by M calculation units of the calculator, M sets of parityvectors, each set includes a plurality (D) of parity vectors.

If M>R then jumping to stage 155 of calculating the M sets of parityvectors in multiple iterations—each iteration includes calculating up toR sets of D parity vectors each.

Stage 150 may include calculating, by each calculation unit and for eachvalue of first index d that ranges between 0 and (D−1), a d'th parityvector of M elements each.

Stage 150 may be followed by stage 160 of calculating the plurality (M)of the redundancy blocks based on the R sets of parity vectors.

Stage 150 may include multiplying (152), by each calculation unit of theR calculation units a corresponding row of the Vandermonde matrix byeach one of D intermediate vectors. Different calculation units multiplydifferent rows of the Vandermonde matrix. If, for example R=M then ther'th calculation unit multiplies the r'th row of the Vandermonde matrix.

Stage 150 may be executed in an iterative manner, wherein during eachiteration each calculation unit calculates a product between aVandermonde matrix coefficient and a word of all intermediate vectorsand add the product to a previously calculated intermediate result.

Accordingly, stage 150 may include performing for each value of a firstindex n that ranges between zero to (N−1):

-   -   a. Reading an n'th block of data and a d'th row, n'th column        coefficient of a Vandermonde matrix.    -   b. Multiplying, in parallel, by calculation units of the        calculator, the d'th row, n'th column coefficient of the        Vandermonde matrix by each word of the n'th block of data to        provide a plurality of current products.    -   c. Adding the plurality of current products to a plurality of        previously calculated results to provide a plurality of        intermediate results to be stored in a buffer.

Due to the parallel processing and the relationship between intermediatevectors and data blocks, during each iteration, a single data block (ora portion thereof) will be processed by each calculation unit.

FIG. 2 illustrates a system 200 according to an embodiment of theinvention.

System 200 may be arranged to execute method 100 of FIG. 1 and method400 of FIG. 4. For simplicity of explanation only the system will beillustrates in relation to the execution of method 100.

System 200 includes a memory unit 210 that is arranged to receive thenumber (M) of redundancy blocks.

System 200 also includes a data distribution unit 212 that is arrangedto distribute data between various components of system 200. Forexample, it is arranged to send data blocks from the memory unit 210 tothe calculator and to send parity vectors to the memory unit or othercomponents.

The memory unit 210 may include a buffer although FIG. 2 illustrates thebuffer 240 as being a separate entity. The buffer 240 is expected to besmaller than the memory unit 210. Data blocks and/or Vandermonde matrixcoefficients can be fetched from the memory unit 210 by a direct memoryaccess (DMA) controller.

System 200 also includes calculator 220 that includes multiple (R)calculation units 222(1)-222(R), that include multiple (R) multipliers224(1)-224(R) and multiple (R) adders 226(1)-226(R). Each multiplier canmultiply various elements (data words, Vandermonde matrix coefficients)in various manners to provide products. It can, for example, perform alogarithmic operation (Log) on the elements to be multiplied, add theoutcome of the logarithmic operation to provide a sum and then performan inverse logarithmic operation (antilog) on the sum to provide theproduct.

A product of each multiplier is added (by an adder) to a previouslycalculated intermediate result (calculated during a last iteration) toprovide a new intermediate result that is sent to buffer 240.

System 200 further includes a controller 230 that is arranged toconfigure the calculator according to M and R.

The memory unit 210 is further arranged to receive multiple (N) datablocks of a plurality (D) of words each. The maximal length of each datablock can be limited to a ratio between the size S of an available spaceof a buffer 240 of system 200 by the number of calculation units thatare currently activated (which is M if M does not exceed R or (if Mexceeds R) by R or X. In FIG. 2 it is assumed that buffer 240 isvirtually partitioned to M parts 240(1)-240(M)−each part allocated to adifferent calculation unit.

If M equals one then the calculation of parity vectors will involveutilizing a single calculation unit. In this case the size S of a datablock can equal the size of the available space of a buffer. Thiscalculation unit calculates one set of D parity vectors.

If M exceeds one but does not exceed R then M calculation units areused. These M calculation units calculate M sets of D parity vectors.

If M equals R*Y+X (Y being a positive integer and X ranges between 1 andR−1) then exceeds R and M modulo R equals a difference X, then thesystem perform at least (Y+1) iterations of calculations. For example,during Y iterations each of the R calculation units may be used tocalculate one set of D parity vectors and during a (Y+1)'th iteration Xcalculation units are used to calculate the remaining X sets of D parityvectors. The M sets of D parity vectors are used to calculate the Mparity blocks.

Whenever M exceeds one different calculation units are arranged tocalculate different sets of parity vectors by multiplying different rowsof a

Vandermonde matrix by intermediate vectors driven from the multiple datablocks.

FIG. 4 illustrates a method 400 according to an embodiment of theinvention.

Method 400 starts by stage 410 of receiving or calculating an invertedmatrix.

The inverted matrix is calculated by inverting a reduced matrix. Thereduced matrix is calculated by reducing M rows of an input matrix thatincludes N+M rows. The input matrix comprises a first group of N rowsand a second group of M rows.

The first group of rows forms a unity matrix. The second group of rowsforms a Vandermonde matrix.

FIG. 6 illustrates input matrix 540, reduced matrix 560 and invertedmatrix 570 according to various embodiments of the invention. In FIG. 6N=4 and M=2. The first group 542 of four rows of input matrix 540 formsa 4×4 unity matrix. The second group 544 of two rows of input matrix 540is the first two rows of a Vandermonde matrix.

It is assumed that the fourth and fifth blocks of six information blocksare corrupted and thus the reduced matrix 560 is generated by deletingthe third and fourth rows of input matrix 540. The deletion isillustrated by matrix 550.

The reduced matrix 560 is inverted to provide inverted matrix 570 thatincludes 4×4 elements denoted INV00-INV33.

Stage 410 is followed by stage 420 of receiving N information blocks bya calculator that comprises multiple (R) calculation units, eachinformation block is D word long.

These N information blocks are selected out of N+M information blocks.Ideally and in an errorless scenario the N+M information blocks shouldhave been equal to N data blocks and M parity blocks written to astorage system (not shown).

Referring to the example set forth in FIG. 5, assuming that D=4, M=2 andN=4 there should have been four data blocks 502 (each data block isillustrated as a four element column of entity 500) and two parityblocks 504 (each parity block is illustrated as a four element column ofentity 500). There are multiple information vectors collectively denoted510 including six information vectors—each information vectors is acolumn that includes 4 elements (N=4), and there are 4×6 informationentities denoted IF00-IF35.

It is assumed that the fourth and fifth information blocks are defective(the fourth and fifth columns of entity 510 are crossed X in FIG. 5) sothe remaining valid information vectors include the first, second,third, and sixth information vectors.

Stage 420 may be followed by stage 430 of converting the N informationblocks to D intermediate vectors, wherein the d'th intermediate vector(index d ranges between zero and D−1) includes the d'th words of eachinformation block.

In FIG. 5 there are four intermediate vectors 521-524.

Stage 430 may be followed by stage 440 of configuring the calculatoraccording to N and R.

If R>N then a sub-set of N calculation units will be utilized.

If R=N all R calculation units will be utilized. If R<N then thefollowing stages will be executed in multiple iterations, each timeutilizing up to R calculation units for multiplying up to R rows of aninverted matrix by intermediate vectors. If, for example N=7 and R=4then during a first iteration four calculation units can be used tomultiply four rows of the inverted matrix by intermediate vectors andduring another iteration three calculation units will be issued tomultiply the three remaining rows of the inverted matrix by intermediatevectors.

Thus, stage 440 may include stage 442 of checking if N exceeds R.

If N does not exceed R then jumping to stage 450 of concurrentlycalculating, by N calculation units of the calculator, M sets ofreconstructed data vectors, each set includes a plurality (D) ofreconstructed data.

If N>R then jumping to stage 455 of calculating the N sets ofreconstructed data vectors in multiple iterations—each iterationincludes calculating up to R sets of D reconstructed data vectors each.

Stage 450 may include calculating, by each calculation unit and for eachvalue of first index d that ranges between 0 and (D−1), a d'threconstructed data vector of N elements each.

Stage 450 may be followed by stage 460 of calculating the plurality (N)of the redundancy blocks based on the R sets of reconstructed datavectors.

Stage 450 may include multiplying (452), by each calculation unit of theR calculation units a corresponding row of the inverted matrix by eachone of D intermediate vectors. Different calculation units multiplydifferent rows of the inverted matrix. If, for example R=N then the r'thcalculation unit multiplies the r'th row of the inverted matrix.

Stage 450 may be executed in an iterative manner, wherein during eachiteration each calculation unit calculates a product between an invertedmatrix coefficient and a word of all intermediate vectors and add theproduct to a previously calculated intermediate result.

Accordingly, stage 450 may include performing for each value of a firstindex n that ranges between zero to (N−1):

-   -   a. Reading an n'th block of data and a d'th row, n'th column        coefficient of an inverted matrix.    -   b. Multiplying, in parallel, by calculation units of the        calculator, the d'th row, n'th column coefficient of the        inverted matrix by each word of the n'th block of data to        provide a plurality of current products.    -   c. Adding the plurality of current products to a plurality of        previously calculated results to provide a plurality of        intermediate results to be stored in a buffer.

FIG. 7 illustrates various data structures according to an embodiment ofthe invention.

FIG. 7 illustrates a first iteration during which the first elementINV00 of the invented matrix is calculated by the first word (IF00,IF01, IF02, IF03) of each of the intermediate vectors 521-524.

FIG. 7 illustrates a second iteration during which the second elementINV00 of the invented matrix is calculated by the second word (IF10,IF11, IF12, IF13) of each of the intermediate vectors 521-524.

FIG. 7 also shows four reconstructed data vectors 531-534 and fourreconstructed data blocks 541-544. These data structures includeselements RDV00-RDV33.

Due to the parallel processing and the relationship between intermediatevectors and data blocks, during each iteration, a single data block (ora portion thereof) will be processed by each calculation unit.

The invention may also be implemented in a computer program for runningon a computer system, at least including code portions for performingsteps of a method according to the invention when run on a programmableapparatus, such as a computer system or enabling a programmableapparatus to perform functions of a device or system according to theinvention. The computer program may cause the storage system to allocatedisk drives to disk drive groups.

A computer program is a list of instructions such as a particularapplication program and/or an operating system. The computer program mayfor instance include one or more of: a subroutine, a function, aprocedure, an object method, an object implementation, an executableapplication, an applet, a servlet, a source code, an object code, ashared library/dynamic load library and/or other sequence ofinstructions designed for execution on a computer system.

The computer program may be stored internally on a non-transitorycomputer readable medium. All or some of the computer program may beprovided on computer readable media permanently, removably or remotelycoupled to an information processing system. The computer readable mediamay include, for example and without limitation, any number of thefollowing: magnetic storage media including disk and tape storage media;optical storage media such as compact disk media (e.g., CD ROM, CD R,etc.) and digital video disk storage media; nonvolatile memory storagemedia including semiconductor-based memory units such as FLASH memory,EEPROM, EPROM, ROM; ferromagnetic digital memories; MRAM; volatilestorage media including registers, memory units or caches, main memory,RAM, etc.

A computer process typically includes an executing (running) program orportion of a program, current program values and state information, andthe resources used by the operating system to manage the execution ofthe process. An operating system (OS) is the software that manages thesharing of the resources of a computer and provides programmers with aninterface used to access those resources. An operating system processessystem data and user input, and responds by allocating and managingtasks and internal system resources as a service to users and programsof the system.

The computer system may for instance include at least one processingunit, associated memory and a number of input/output (I/O) devices. Whenexecuting the computer program, the computer system processesinformation according to the computer program and produces resultantoutput information via I/O devices.

In the foregoing specification, the invention has been described withreference to specific examples of embodiments of the invention. It will,however, be evident that various modifications and changes may be madetherein without departing from the broader spirit and scope of theinvention as set forth in the appended claims.

Moreover, the terms “front,” “back,” “top,” “bottom,” “over,” “under”and the like in the description and in the claims, if any, are used fordescriptive purposes and not necessarily for describing permanentrelative positions. It is understood that the terms so used areinterchangeable under appropriate circumstances such that theembodiments of the invention described herein are, for example, capableof operation in other orientations than those illustrated or otherwisedescribed herein.

The connections as discussed herein may be any type of connectionsuitable to transfer signals from or to the respective nodes, units ordevices, for example via intermediate devices. Accordingly, unlessimplied or stated otherwise, the connections may for example be directconnections or indirect connections. The connections may be illustratedor described in reference to being a single connection, a plurality ofconnections, unidirectional connections, or bidirectional connections.However, different embodiments may vary the implementation of theconnections. For example, separate unidirectional connections may beused rather than bidirectional connections and vice versa. Also,plurality of connections may be replaced with a single connection thattransfers multiple signals serially or in a time multiplexed manner.Likewise, single connections carrying multiple signals may be separatedout into various different connections carrying subsets of thesesignals.

Therefore, many options exist for transferring signals.

Although specific conductivity types or polarity of potentials have beendescribed in the examples, it will be appreciated that conductivitytypes and polarities of potentials may be reversed.

Each signal described herein may be designed as positive or negativelogic. In the case of a negative logic signal, the signal is active lowwhere the logically true state corresponds to a logic level zero. In thecase of a positive logic signal, the signal is active high where thelogically true state corresponds to a logic level one. Note that any ofthe signals described herein may be designed as either negative orpositive logic signals. Therefore, in alternate embodiments, thosesignals described as positive logic signals may be implemented asnegative logic signals, and those signals described as negative logicsignals may be implemented as positive logic signal.

Furthermore, the terms “assert” or “set” and “negate” (or “deassert” or“clear”) are used herein when referring to the rendering of a signal,status bit, or similar apparatus into its logically true or logicallyfalse state, respectively. If the logically true state is a logic levelone, the logically false state is a logic level zero. And if thelogically true state is a logic level zero, the logically false state isa logic level one.

Those skilled in the art will recognize that the boundaries betweenlogic blocks are merely illustrative and that alternative embodimentsmay merge logic blocks or circuit elements or impose an alternatedecomposition of functionality upon various logic blocks or circuitelements. Thus, it is to be understood that the architectures depictedherein are merely exemplary, and that in fact many other architecturesmay be implemented which achieve the same functionality.

Any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality may be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality

Furthermore, those skilled in the art will recognize that boundariesbetween the above described operations merely illustrative. The multipleoperations may be combined into a single operation, a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of a particular operation,and the order of operations may be altered in various other embodiments

Also for example, in one embodiment, the illustrated examples may beimplemented as circuitry located on a single integrated circuit orwithin a same device. Alternatively, the examples may be implemented asany number of separate integrated circuits or separate devicesinterconnected with each other in a suitable manner.

Also for example, the examples, or portions thereof, may implemented assoft or code representations of physical circuitry or of logicalrepresentations convertible into physical circuitry, such as in ahardware description language of any appropriate type.

Also, the invention is not limited to physical devices or unitsimplemented in non-programmable hardware but can also be applied inprogrammable devices or units able to perform the desired devicefunctions by operating in accordance with suitable program code, such asmainframes, minicomputers, servers, workstations, personal computers,notepads, personal digital assistants, electronic games, automotive andother embedded systems, cell phones and various other wireless devices,commonly denoted in this application as ‘computer systems.

However, other modifications, variations and alternatives are alsopossible. The specifications and drawings are, accordingly, to beregarded in an illustrative rather than in a restrictive sense.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word ‘comprising’ does notexclude the presence of other elements or steps then those listed in aclaim. Furthermore, the terms “a” or “an,” as used herein, are definedas one or more than one. Also, the use of introductory phrases such as“at least one” and “one or more” in the claims should not be construedto imply that the introduction of another claim element by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases “oneor more” or “at least one” and indefinite articles such as “a” or “an.”The same holds true for the use of definite articles. Unless statedotherwise, terms such as “first” and “second” are used to arbitrarilydistinguish between the elements such terms describe. Thus, these termsare not necessarily intended to indicate temporal or otherprioritization of such elements The mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

1-32. (canceled)
 33. (canceled)
 34. A system comprising: a calculatorthat comprises a plurality of calculation units and a buffer having abuffer size; and a controller for configuring the calculator in aredundancy calculation mode to calculate one or more redundancy blocksfor data blocks, wherein in the redundancy calculation mode: thecontroller is arranged to configure the calculator by determining a sizeof each data block based on a ratio between the buffer size and a numberof activated calculation units in the redundancy calculation mode; andthe calculator is arranged to: calculate one or more sets of parityvectors by at least a subset of the calculation units of the calculator,wherein each set of parity vectors includes the same number of parityvectors as the number of words in each data block; and calculate the oneor more redundancy blocks based on the one or more sets of parityvectors.
 35. The system according to claim 34, wherein in the redundancycalculation mode, different calculation units calculate different setsof parity vectors by multiplying different rows of a Vandermonde matrixby intermediate vectors.
 36. The system according to claim 34, whereindifferent numbers of redundancy blocks represent different redundantarray of independent disks (RAID) levels.
 37. The system according toclaim 34, wherein the plurality of calculation units includes at leastfour calculation units.
 38. A system comprising: a calculator thatcomprises a plurality of calculation units and a buffer having a buffersize; and a controller for configuring the calculator in areconstruction mode to generate reconstructed data blocks, wherein inthe reconstruction mode: the controller is arranged to configure thecalculator by determining a size of each reconstructed data block inresponse to a ratio between the buffer size and a number of activatedcalculation units in the reconstruction mode; and the calculator isarranged to: calculate one or more sets of reconstructed data vectors byat least a subset of the calculation units of the calculator, whereineach set of reconstructed data vectors includes the same number ofreconstructed data vectors as the number of words in each data block;and generate the one or more reconstructed data blocks based on the oneor more sets of reconstructed data vectors.
 39. The system according toclaim 38, wherein in the reconstruction mode, different calculationunits calculate different sets of reconstructed data vectors bymultiplying different rows of an inverted matrix by intermediatevectors.
 40. The system according to claim 38, wherein the plurality ofcalculation units includes at least four calculation units.
 41. A methodfor calculating one or more redundancy blocks for data blocks, themethod comprising: receiving the data blocks by a calculator thatcomprises a plurality of calculation units and a buffer having a buffersize; configuring the calculator by determining a size of each datablock based on a ratio between the buffer size and a number of activatedcalculation units; calculating one or more sets of parity vectors by atleast a subset of the calculation units of the calculator, wherein eachset of parity vectors includes the same number of parity vectors as thenumber of words in each data block; and calculating the one or moreredundancy blocks based on the one or more sets of parity vectors. 42.The method according to claim 41, wherein the number of redundancyblocks being calculated is equal to the number of calculation units. 43.The method according to claim 41, wherein the number of redundancyblocks being calculated is smaller than the number of calculation units.44. The method according to claim 41, wherein the one or more sets ofparity vectors include a single set of parity vectors calculated by asingle calculation unit, and one redundancy block is calculated based onthe single set of parity vectors.
 45. The method according to claim 41,wherein the step of calculating the one or more sets of parity vectorsincludes: selecting a certain set of rows of a Vandermonde matrix; andcalculating the sets of parity vectors by processing the certain set ofrows of the Vandermonde matrix.
 46. The method according to claim 45,wherein different calculation units calculate different sets of parityvectors by multiplying different rows of the Vandermonde matrix byintermediate vectors.
 47. The method according to claim 41, whereindifferent numbers of redundancy blocks represent different redundantarray of independent disks (RAID) levels.
 48. The method according toclaim 41, wherein the plurality of calculation units includes at leastfour calculation units.
 49. The method according to claim 41, furthercomprising receiving multiple coefficients of a Vandermonde matrix indescriptors of the data blocks.
 50. A method for generating one or morereconstructed data blocks, the method comprising: receiving anindication of the number of data blocks to be reconstructed by acalculator that comprises a plurality of calculation units and a bufferhaving a buffer size; configuring the calculator by determining a sizeof each reconstructed data block in response to a ratio between thebuffer size and a number of activated calculation units; calculating oneor more sets of reconstructed data vectors by at least a subset of thecalculation units of the calculator, wherein each set of reconstructeddata vectors includes the same number of reconstructed data vectors asthe number of words in each data block; and generating the reconstructeddata blocks based on the one or more sets of reconstructed data vectors.51. The method according to claim 50, wherein the number of data blocksbeing reconstructed is equal to the number of calculation units.
 52. Themethod according to claim 50, wherein the number of data blocks beingreconstructed is smaller than the number of calculation units.
 53. Themethod according to claim 50, wherein the one or more sets ofreconstructed data vectors include a single set of reconstructed datavectors calculated by a single calculation unit, and one reconstructeddata block is calculated based on the single set of reconstructed datavectors.
 54. The method according to claim 50, wherein the step ofcalculating the one or more sets of reconstructed data vectors includes:selecting a certain set of rows of an inverted matrix, wherein theinverted matrix is calculated by inverting a reduced matrix, and thereduced matrix is calculated based on an input matrix that comprises aunity matrix and a Vandermonde matrix; and calculating the sets ofreconstructed data vectors by the calculation units by processing thecertain set of rows of the inverted matrix.
 55. The method according toclaim 54, wherein different calculation units calculate different setsof reconstructed data vectors by multiplying different rows of theinverted matrix by intermediate vectors.